Density estimation with distribution element trees

Density estimation with distribution element trees

The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient methods are needed. We propose a new method that is based on a decomposition of the distribution to be estimated in terms of so-called distribution elements (DE...

Density Estimation Trees

Density estimation is one of the fundamental tasks in statistics and machine learning, as it often appears as a subroutine in tasks such as regression, classification, and clustering. However, density estimation in high dimensions remains a challenging problem due to the curse of dimensionality, which affects the convergence rates of many popular density estimation techniques. In addition, comm...

Efficient Estimation of the Density and Cumulative Distribution Function of the Generalized Rayleigh Distribution

The uniformly minimum variance unbiased (UMVU), maximum likelihood, percentile (PC), least squares (LS) and weighted least squares (WLS) estimators of the probability density function (pdf) and cumulative distribution function are derived for the generalized Rayleigh distribution. This model can be used quite effectively in modelling strength data and also modeling general lifetime data. It has...

Smoothing Spline Density Estimation : Conditional Distribution

This article extends recent developments in penalized likelihood probability density estimation to the estimation of conditional densities on generic domains. Positivity and unity constraints for a probability density are enforced through a one-to-one logistic conditional density transform made possible by term trimming in an ANOVA decomposition of multivariate functions. The construction of mo...

Imanol Studer ( 09 - 734 - 575 ) Density Estimation Trees